Respuesta :
Answer:
[tex]z=\frac{0.0903 -0.1}{\sqrt{\frac{0.1(1-0.1)}{310}}}=-0.569[/tex]
The p value for this case can be calculated with this probability:
[tex]p_v =P(z<-0.569)=0.285[/tex]
Since the p value is higher than significance level we don't have enough evidence to conclude that the true proportion is significantly less than 0.1
Step-by-step explanation:
Information given
n=310 represent th sample selected
X=28 represent the subjects wrong
[tex]\hat p=\frac{28}{310}=0.0903[/tex] estimated proportion of subjects wrong
[tex]p_o=0.1[/tex] is the value to verify
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to test the claim that less than 10 percent of the test results are wrong ,and the hypothesis are:
Null hypothesis:[tex]p\geq 0.1[/tex]
Alternative hypothesis:[tex]p < 0.1[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info we got:
[tex]z=\frac{0.0903 -0.1}{\sqrt{\frac{0.1(1-0.1)}{310}}}=-0.569[/tex]
The p value for this case can be calculated with this probability:
[tex]p_v =P(z<-0.569)=0.285[/tex]
Since the p value is higher than significance level we don't have enough evidence to conclude that the true proportion is significantly less than 0.1
